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Section 3-3 The Addition Rule

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Section 3-3

The Addition Rule

Addition Rule – “or”

The probability that A or B.One eventMutually Exclusive:

P(A or B) = P(A) + P(B)

Mutually Exclusive events – two events that cannot happen at the same time

What is the probability of rolling a number on a die less than 3 or more than 3?

4 5

2 3

6833

Page 4: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Example #1

A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-flites, find the probability…

a. A golf ball is a Titleist or Maxfli.b. A golf ball is a Maxfli or Top-Flite.c. A golf ball is not a Top-Flite.

Page 5: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Example 2

A standard deck of cards contains 52 cards. One card is randomly selected from the deck. What is the probability..

a. Of randomly selecting a heart or club.

b. Of randomly selecting a 5,6, or 7.

Page 6: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Not Mutually Exclusive – Two events that can happen at the same time, two events that have something in common

What is the probability of rolling a number on a die less than 5 or more than 3?

1 2 4

4 3 1

6100

Page 7: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Mutually Exclusive or

Not Mutually Exclusive?

S = {1,2,3,4,5,6,7,8,9,10,11,12}E = {2,3,4,5,6,7} F = {5,6,7,8,9}G = {9,10,11,12} H = {2,3,4}

1. Are E and F mutually exclusive?2. Are F and G mutually exclusive?3. Are E and G mutually exclusive?4. Are F and H mutually exclusive?

Addition Rule – “or”

The probability that A or B.One eventNot Mutually Exclusive:

P(A or B) = P(A) + P(B) – P(A and B)

Page 9: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Randomly select an individual who is either male or wearing black

NOT mutually exclusive because some (2) of the males are black …

Page 10: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Find the probability of randomly selecting a female or seated.

Page 11: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Find the probability of randomly selecting a female or wearing black.

Page 12: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Roll a Die …

Find the probability of rolling an even number or a number greater than 3.

Page 13: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or a boy.

Page 14: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or survived.

Page 15: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Find the probability of randomly selecting one person from the Titanic roster, and that person being a woman or survived.

Page 16: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Ticket Issued

No Ticket Issued

Total

Speeding 40 170 210

No Taillights 10 35 45

No Signal 5 25 30

Careless Driving 45 70 115

Total 100 300 400

1. What is the probability that a ticket was issued?

2. What’s the probability a car did not have taillights?

3. What’s the probability a driver will get a ticket, given that they were stopped for careless driving?

4. What the probability a person was stopped for speeding or failure to use signals?

Page 17: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Mixed Practice Ticket Issued

No Ticket Issued

Total

Speeding 40 170 210

No Taillights 10 35 45

No Signal 5 25 30

Careless Driving 45 70 115

Total 100 300 400

5. Given a ticket was not issued, what’s the probability a person was stopped for speeding?

6. What’s the probability that the first person got a speeding ticket and the second person got a ticket for no signal?

Page 18: Section 3-3 The Addition Rule. Addition Rule – “or” The probability that A or B. One event Mutually Exclusive: P(A or B) = P(A) + P(B)

Homework:

HW p 136, #15 - 20Quiz tomorrow on conditional probability

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